The announcement was made on the Duke and Duchess of Sussex's recently launched Instagram account.
"We are pleased to announce that Their Royal Highnesses The Duke and Duchess of Sussex welcomed their firstborn child in the early morning on May 6th, 2019," the statement reads.
"Their Royal Highnesses’ son weighs 7lbs. 3oz."
The announcement adds that the duchess and the newborn are both "healthy and well".
"The couple thank members of the public for their shared excitement and support during this very special time in their lives."
More information about the birth of the royal baby will be shared with the public in the coming days.
Prince Harry made an announcement in Windsor that he and Meghan have had a baby boy.
"I’m very excited to announce that Meghan and myself had a baby boy earlier this morning, a very healthy boy," the duke said.
"Mother and baby are doing incredibly well. It’s been the most amazing experience I could ever have possibly imagined.
"How any woman does what they do is beyond comprehension, but we’re both absolutely thrilled and so grateful for all the love and support from everybody out there. It’s been amazing, so I just wanted to share this with everybody."
The royal couple are currently at Frogmore Cottage with their newborn baby and the Duchess of Sussex's mother, Doria Ragland.
"The Duchess's mother, Doria Ragland, who is overjoyed by the arrival of her first grandchild, is with Their Royal Highnesses at Frogmore Cottage," the royal family said in a statement released on Twitter.
"Her Royal Highness and the baby are both doing well."
Buckingham Palace has announced that the Queen, the Duke of Edinburgh and other members of the royal family have been informed of the birth.
"The Queen, The Duke of Edinburgh, The Prince of Wales, The Duchess of Cornwall, The Duke and Duchess of Cambridge, Lady Jane Fellowes, Lady Sarah McCorquodale and Earl Spencer have been informed and are delighted with the news," the palace stated.
According to Shutterstock royal photographer Tim Rooke, it will likely be a short while before pictures of the royal baby are released.
“I don't know when I will be allowed to take the first pictures. I imagine the first pictures will be released via the royal rota," Rooke tells The Independent.
"They may decide to do a photo call, which could be quite a while from now, as I imagine that the christening will also be private."
Rooke adds that he believes the public are "genuinely happy" for the Duke and Duchess of Sussex. "People seem to have a genuine affection for Harry and Meghan," he said.
Royal biographer Penny Juror believes Prince Harry has been "quite clever" about ensuring that he and Meghan can enjoy the birth of their child in private.
"Now that it's happened, there he was saying it has happened and how exciting it was, which is great, but he did not want the whole circus standing outside the labour ward talking vacuously into television cameras while his poor wife laboured away. So he got what he wanted," Juror tells The Independent.
“I think there’s every likelihood that they will keep the press at arm’s length and do this in their own way. Harry is very very careful of his privacy."
A framed notice in honour of the birth of the Duke and Duchess of Sussex's baby has been placed on a ceremonial easel on the forecourt of Buckingham Palace.
The baby is seventh in line to the throne and is Queen Elizabeth II’s eighth great-grandchild.
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